On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation

Daescu, Dacian N.
August 2008
Monthly Weather Review;Aug2008, Vol. 136 Issue 8, p3050
Academic Journal
The equations of the forecast sensitivity to observations and to the background estimate in a four-dimensional variational data assimilation system (4D-Var DAS) are derived from the first-order optimality condition in unconstrained minimization. Estimation of the impact of uncertainties in the specification of the error statistics is considered by evaluating the sensitivity to the observation and background error covariance matrices. The information provided by the error covariance sensitivity analysis is used to identify the input components for which improved estimates of the statistical properties of the errors are of most benefit to the analysis and forecast. A close relationship is established between the sensitivities within each input pair data/error covariance such that once the observation and background sensitivities are available the evaluation of the sensitivity to the specification of the corresponding error statistics requires little additional computational effort. The relevance of the 4D-Var sensitivity equations to assess the data impact in practical applications is discussed. Computational issues are addressed and idealized 4D-Var experiments are set up with a finite-volume shallow-water model to illustrate the theoretical concepts. Time-dependent observation sensitivity and potential applications to improve the model forecast are presented. Guidance provided by the sensitivity fields is used to adjust a 4D-Var DAS to achieve forecast error reduction through assimilation of supplementary data and through an accurate specification of a few of the background error variances.


Related Articles

  • Finitistic Arithmetic and Classical Logic†. Ganea, Mihai // Philosophia Mathematica;Jun2014, Vol. 22 Issue 2, p167 

    It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational...

  • How Abstract Is Symbolic Thought? Landy, David; Goldstone, Robert L. // Journal of Experimental Psychology. Learning, Memory & Cognition;Jul2007, Vol. 33 Issue 4, p720 

    In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated...

  • Inter-Student Questioning in Students' Investigations into Algebra: A Dialogue Between Kianja and Jerel. Lai, F. Frank // Conference Papers -- Psychology of Mathematics & Education of No;2006 Annual Meeting, p1 

    My study investigates the mathematical behaviors that students engage to decide on the validity of their fellow students' ideas and reasoning. To do so, I examine an 11-minute video clip of five students, focusing on Kianja and Jerel, who argue about the equations corresponding to points...

  • The Evolution of Formal Mathematical Reasoning: A Case Study of Uniqueness in Differential Equations. Rasmussen, Chris // Conference Papers -- Psychology of Mathematics & Education of No;2004 Annual Meeting, Toronto, CA, p1 

    The purpose of this research report is to describe key processes by which students come to understand and apply the uniqueness theorem for first order differential equations. More generally, I frame the analysis as a paradigm case for the emergence of formal mathematical reasoning. Analysis of...

  • Formalized reasoning method for assembly sequences based on Polychromatic Sets theory. Zhao, Shanshan; Li, Zongbin // International Journal of Advanced Manufacturing Technology;Oct2009, Vol. 42 Issue 9/10, p993 

    This paper presents a new formalized reasoning method for assembly sequences generation which reduces the solution space dramatically. Firstly, a polychromatic sets (PS) matrix is introduced to describe the relations between the part-match and freedom; Secondly, the polychromatic sets matrix of...

  • Significance Testing with No Alternative Hypothesis: A Measure of Surprise. Howard, J. // Erkenntnis;Mar2009, Vol. 70 Issue 2, p253 

    A pure significance test would check the agreement of a statistical model with the observed data even when no alternative model was available. The paper proposes the use of a modified p-value to make such a test. The model will be rejected if something surprising is observed (relative to what...

  • Randomized Arguments are Transferable†. Jackson, Jeffrey C. // Philosophia Mathematica;Oct2009, Vol. 17 Issue 3, p363 

    Easwaran has given a definition of transferability and argued that, under this definition, randomized arguments are not transferable. I show that certain aspects of his definition are not suitable for addressing the underlying question of whether or not there is an epistemic distinction between...

  • Errata.  // UMAP Journal;Winter2012, Vol. 33 Issue 4, p399 

    Several corrections to the articles including "Finding Vintage Concentrations in a Sherry Solera," published in the 1990 issue, "Mathserve Lives On!," published in the 2004 issue, and "Author's Commentary: The Outstanding Kidney Exchange Papers," published in the 2007 issue are presented.

  • Category-based Equational Reasoning: An Approach to Ontology Integration. GELDART, JOE; SONG, WILLIAM // Journal of Logic & Computation;Oct2009, Vol. 19 Issue 5, p791 

    Incorporating dynamic, general computational knowledge into Semantic Web ontologies is becoming increasingly important. The Semantic Web is now being used to model the behaviour of highly dynamic domains such as web-services, but current approaches to ontologies [such as Web Ontology Language...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics